## The expected delay and queue length distribution for systems such as fixed-cycle traffic light system without finding roots

Anna Oblakova, UT-EWI-SOR

## Abstract:

For many discrete-time queuing systems the pgf of the queue length is represented as a fraction with *n* unknown variables. The denominator of the fraction in these systems has *n* zeros inside and on the unit circle. Since the pgf is analytic inside the unit disk and continuous up to the unit circle, the zeros of the denominator should be also zeros of the numerator. Thus, the common approach to find the unknown variables includes finding this zeros. However, this procedure is quite time-consuming.

In our talk we present a method how to find the expectation and distribution of the queue length without finding the zeros for models such as the fixed-cycle traffic light model and the bulk-service queue model.